杏吧传媒 数学大讲坛第二期

第十二讲——南京师范大学李丹博士后学术报告

题目：Recent developments of weak Galerkin finite element methods for PDEs

时间：2023年4月14日（周五）上午9:30——11:00

地点：腾讯会议(会议ID：351735811）

报告人：李丹博士后

摘要：In this talk, we will discuss the recent progress on the weak Galerkin (WG) methods and its applications. A mathematical analysis is established for the WG methods for the Poisson equation with Dirichlet boundary value when the curved elements are involved on the interior edges of the finite element partition or/and on the boundary of the whole domain in two dimensions. A new WG method is proposed to extend the well-known Morley element for the biharmonic equation from triangular elements to general polytopal elements. A new Lp-primal-dual WG method with p > 1 is proposed for the first-order transport problems. The generalized weak Galerkin method is proposed and analyzed for the biharmonic equation that can allow arbitrary combinations of piecewise polynomial functions defined in the interior and on the boundary of general polygonal or polyhedral elements. A series of numerical results are presented to verify the efficiency and accuracy of the numerical methods.

报告人简介：

李丹，2022年博士毕业于西北工业大学数学与统计杏吧传媒 ，目前在南京师范大学从事博士后研究。主要从事偏微分方程新方法的设计与分析。与合作者在弱Galerkin有限元方法领域做出了一些重要的研究工作，相关研究成果发表在NMPDE、CMA、JCAM等国际计算数学期刊上。